SOLUTION: The function f(x)=2x/3x-5 is one-to-one. find its inverse and check your answer

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Question 838748: The function f(x)=2x/3x-5 is one-to-one. find its inverse and check your answer

Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse we can solve for x to convert it to the dependent variable:
y=%28+2x+%29%2F%283x-5%29
%283x-5%29y=+2x+

3xy-5y=+2x+

3xy-2x=++5y

x%283y-2%29=++5y

x=++%285y%29%2F%283y-2%29
Once their roles have reversed, the resulting expression is the inverse:
g%28x%29=%285x%29%2F%283x-2%29
To check we take the two appropriate inverses to see if they each recover the input (i.e. x).

Checking...
f%28g%28x%29%29=%282%28%285x%29%2F%283x-2%29%29%29%2F%283%28%285x%29%2F%283x-2%29%29-5%29




f%28g%28x%29%29=%28%2810x%29%2F%283x-2%29%29%2A%28%283x-2%29%2F%2815x-15x%2B10%29%29=x